Python softmax实现及数值稳定性详解

import numpy as np
def softmax(x):
"""Compute the softmax of vector x."""
    exp_x = np.exp(x)
    softmax_x = exp_x / np.sum(exp_x)
    return softmax_x

softmax([1, 2, 3])
array([0.09003057, 0.24472847, 0.66524096])

softmax([1000, 2000, 3000])
array([nan, nan, nan])

import numpy as np
def softmax(x):
"""Compute the softmax in a numerically stable way."""
    x = x - np.max(x)
    exp_x = np.exp(x)
    softmax_x = exp_x / np.sum(exp_x)
    return softmax_x

softmax([1000, 2000, 3000])
array([ 0.,  0.,  1.])

import numpy as np
def softmax(x):
    """
    Compute the softmax function for each row of the input x.
    Arguments:
    x -- A N dimensional vector or M x N dimensional numpy matrix.
    Return:
    x -- You are allowed to modify x in-place
    """
    orig_shape = x.shape
    if len(x.shape) > 1:
        # Matrix
        exp_minmax = lambda x: np.exp(x - np.max(x))
        denom = lambda x: 1.0 / np.sum(x)
        x = np.apply_along_axis(exp_minmax,1,x)
        denominator = np.apply_along_axis(denom,1,x) 
        if len(denominator.shape) == 1:
            denominator = denominator.reshape((denominator.shape[0],1))
        x = x * denominator
    else:
        # Vector
        x_max = np.max(x)
        x = x - x_max
        numerator = np.exp(x)
        denominator =  1.0 / np.sum(numerator)
        x = numerator.dot(denominator)
    assert x.shape == orig_shape
    return x